Question

How much money would need to be deposited into an account earning 5.75% interest compounded annually in order for the accumulated value at the end of 25 years to be $85,000? a. $75,425.52 b. $59,130.43 c. $21,009.20 d. $20,258.70

Answer 1

Answer:

c. $21009.20

Step-by-step explanation:

We are asked to find the principal amount of money that would be needed to deposited into an account earning 5.75% interest compounded annually in order for the accumulated value at the end of 25 years to be $85,000.

We will use compound interest formula to solve our given problem.

$A=P(1+\frac{r}{n})^{nT}$, where,

A = Final amount after T years,

P = Principal amount,

r = Interest rate in decimal form,

n = Number of times interest is compounded per year,

T = Time in years.

Let us convert our given interest rate in decimal form.

$5.75\%=\frac{5.75}{100}=0.0575$

Upon substituting our given values in compound interest formula we will get,

$\ 85,000=P(1+\frac{0.0575}{1})^{1*25}$

$\ 85,000=P(1+0.0575)^{25}$

$\ 85,000=P(1.0575)^{25}$

$\ 85,000=P*4.0458464965061301$

Let us divide both sides of our equation by 4.0458464965061301.

$\frac{\ 85,000}{4.0458464965061301}=\frac{P*4.0458464965061301}{4.0458464965061301}$

$\ 21009.20044134235=P$

Upon rounding our answer to nearest hundredth we will get,

$P\approx \ 21009.20$

Therefore, an amount of $21009.20 should be deposited in the account and option 'c' is the correct choice.

Answer 2

I will assume you are using compound interest. 

let the amount invested be x 

x(1.0575)^25 = 85000 
x = 85000/1.0575^25 = $21,009.20